Contact mechanics of coated substrates

Analytical contact mechanics models were developped and applied to the stress analysis of confined polymer films under indentation loading. These approaches have been extended to adhesive contacts of thin films.

With C. Fretigny and Etienne Barthel (SVI Saint Gobain)
 

We have addressed the problem of the calculation of the elastic stress and displacement field within isotropic layered media in frictionless contact with rigid axisymmetric indenters. For a prescribed surface stress distribution, the integral transform approach is recalled using a matrix formulation which lends itself to generalizations to multilayered systems. It leads to an analytical solution for the Hankel transform of the elastic field which can readily be numerically inverted in the real space using available discrete Hankel transform algorithms.

Shear stress distribution within a thin film confined between elastic substrates
 

Other investigations address the problem of adhesive contacts between layered substrates and axisymetric probes. A semi-analytical approach to adhesive contacts has been developed as an extension of a model recently published by Perriot and Barthel [Perriot, A. and Barthel, E. J Mat Res, 2004. 19(2) : 600-608] for the axisymetric elastic indentation of non adhesive, coated substrates. In addition to the load and penetration at equilibrium, the model allowed deriving the shape of the free surface in the contact zone. The validity of the approach was verified from experiments using contacts between acrylate films above their glass transition temperature (Tg) and spherical glass lenses. When the adhesive contacts were quenched below Tg, stable imprints were obtained which allowed to determine the surface deformation of the films. The latter were found consistent with the hypothesis of short range surface forces which was embedded in the contact model. Deviations from the theory in the form of fingering instabilities at the periphery of the contact were observed when the confinement of the film was increased. A calculation of the stresses within the adhesive contacts indicated that these instabilities are probably driven by the release of lateral constraints within the confined films.

Deformation of te surface of a thin adhesive film contacting a spherical glass probe.

Publications

A. Chateauminois, C. Fretigny and E. Gacoin
Mechanical properties of thin polymer films
in Polymer Tribology, S. Sinha and B.J. Briscoe Eds, Imperial College Press, 2009
 

C. Fretigny and A. Chateauminois
Solution for the elastic field in a layered medium under axisymetric contact loading
Journal of Physics D 40 (2007) 5418-5426
 

E. Barthel, A. Perriot, A. Chateauminois, C. Fretigny
Elastic contact to nearly incompressible coatings - Stiffness enhancement and elastic pile-up
Philosophical Magazine 86 , N°33-35 (2006) 5359-5369
 

P.Mary, A. Chateauminois, C. Fretigny
Contact deformation of elastic coatings in adhesive contacts with spherical probes
J Physics D : Applied Physics 39 (2006) 3665-3673